The region of physical feasibility of heat exchange systems in the space of their thermodynamic indicators (heat load, dissipation, and thermal conductivity) is constructed in this work. Criteria of thermodynamic perfection for typical two-flow cells are calculated. A condition of thermodynamic equivalence of heat exchange systems is given, and an algorithm for constructing a multiflow system equivalent to a two-flow heat exchanger is proposed. The cases of variable heat capacity, change of the phase state, and different flow hydrodynamics are considered. The constraints on the temperatures of all or some of the flows at the inlet and outlet of the heat exchange system are taken into account. The synthesis involves the choice of the structure of contacts, the values of free parameters of flows, and the distribution of contact areas and heat loads between two-flow heat exchange cells.